Beyond Disavowing the Politics of Equity and Quality in Mathematics Education
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BEYOND DISAVOWING THE POLITICS OF EQUITY AND QUALITY IN MATHEMATICS EDUCATION
Alexandre Pais Paola Valero
Aalborg University
INTRODUCTION The purpose of this article is to provide a deeper theoretical understanding of how the problem of equity, and its relation with the issue of quality, is addressed in mathematics education research. We adopt a sociopolitical perspective, meaning that we situate mathematics education as part of the larger social, political and historical network of social practices (Valero, 2002, 2004). The need for research that grasps the interplay between the macro-sociological space and the more focalized practices of mathematical teaching and learning has been acknowledged in important publications (e.g. English, 2008; Menghini, Furinghetti, Giacardi, & Arzalello (2008)), particularly when the issue is equity (e. g. Gutiérrez, 2007; Anderson & Tate, 2008; Nasir & Cobb, 2002).
It is widely recognized in mathematics education research that issues of social justice, democracy, inclusion or diversity are political in their nature and extend beyond mathematics education. However, the great majority of mathematics education research, by being focused on more pragmatic approaches, lacks a theoretical comprehension of how the problems it tries to solve are related with broader social and political structures. As mentioned by Baldino and Cabral (2006), there is the risk of moving blindly if we, as researchers, do not “take a certain distance and develop consistent research theoretical frameworks to appreciate our practices” (p. 31). In this article we will make a contribution to this comprehension, by analyzing how social discourses and forms of ideology can permeate the way mathematics education research engages on the issues of equity and quality.
We take support on the philosophy of Michel Foucault, Giorgio Agamben and Slavoj Žižek. The first two provides us the theoretical framework to situate mathematics education research in a broader historical trend coined by Foucault as bio-politics, involving both dispositives of individualization and globalization. Slavoj Žižek, on the other hand, gives us the theoretical support to understand how ideology permeates today the field of mathematics education research.
We start by situating our analysis as part of a concern with the way theory is conceived in mathematics education research. We argue that theory is mostly applied in relation to learning, and situate this tendency in a broader social propensity to reduce political dimensions of life to a matter of effective social administration, informed by specialized social sciences. Afterwards we analyze recent mathematics education research on equity focusing on the way it perceives its role and the different ways suggested for solving the problem of inequity. We notice how research tends to address this problem as a matter of developing the best “instructional methods” to allow mathematical success to all students, and suggest a justification for this: the field is constituted by a dangerous exclusion of its educational dimension. Mathematics education research owns specificity to mathematics and in this process disavows engaging on research that addresses problems that are not specific of school mathematics. This way of conceiving the field encloses an inconsistency concerning equity: we know that equity is an economical and political problem that surpasses school mathematics; nevertheless we continue to research it as a specific problem of mathematics education. In the last pages we explore the ideology behind this inconsistency and argue for the need for mathematics education to explore theories and approaches that posit inequity not as a marginal problem of capitalism, but a condition for it.
OUR CONCERN AND APPROACH The motivation to write this article is part of a broader concern that we as mathematics educators researchers have regarding the way the majority of research in mathematics education is carried out. In recent articles (Pais, Stentoft & Valero, 2009, 2010) we developed a critique on the way theory is used in mathematics education research. We argued that there is a strong tendency to reduce the understanding of theory in mathematics education research to a matter of learning. This trend is not exclusive to the field of mathematics education research, but has over the last two decades also proliferated in broader discourses of education. The language of education has largely been replaced by a technical language of learning (Biesta, 2005). The contradictions on the role of school and the goals of education that fueled part of the educational debate during the last century 1 seem to have been surpassed. We seem to have reached a consensus on the benefits of schooling, we need to make it more effective and, therefore, we live an apparent consensus in what concerns education. The problems with schooling and school subjects are not anymore to be political or ideological, but have become primarily technical or didactical. In most cases, solutions to educational problems are being reduced to better methods and techniques to teach and learn, to improve the use of technology, to assess student’s performance, etc. Education has progressively been reduced to be a controllable, designable, engineerable and operational framework for the individual’s cognitive change. Although the prevalence of theory as “learning theory” has allowed us to gain deeper knowledge on the processes of teaching and learning mathematics, we suggest that it has left important problems faced by the educational communities in their everyday practices unaddressed. We argue that in order to bring these problems seriously into the gaze of research, we need a broader theoretical frame which allows us to understand theory not just as “theory of learning”, but also as “theory of education”.
This reduction disavows the political magnitude of education. Learning is conceived as a nominal activity, isolated from what Valero (2004) calls the network of sociopolitical practices of mathematics education. That is, the entire social, political, economical and historical framework that gives sense to the practices of mathematics education.
This tendency to erase political considerations from educational research is part of a larger societal trend where fundamental social problems are addressed as if they were the object of expert management and administration (Foucault, 1978; Agamben, 1998). Foucault (1977, 1978) shows us that this government of life is achieved through two fundamental technologies that act upon the
1 For instance the discussions fueled by the work of John Dewey, Ivan lllich, Louis Althusser or Paulo Freire. individual and the population. On the one hand, the technologies of the self refers to the process of subjectification that forces the individual to bind himself to his own identity, defined by the degree of adherence to social norms. On the other hand, the political techniques or bio-power refers to the way the State assumes and integrates the care of natural life of individuals into its very center.
As an example of the first, we can think about the mathematical curriculum as a technology of the self. Popkewitz (2004), in his incursion into mathematics education, brought out the mechanisms through which the alchemy of school mathematics constructs a set of learning standards that are closer related to the administration of children rather than with an agenda of mathematical knowledge. This alchemy is carried out by pedagogy (psychology and social psychology that generate knowledge about the children) that appropriates the mathematical content to transmit competences, behaviors and attitudes (e.g., being participative, competent, having self-esteem). In this perspective, school mathematics serves as an alibi to the appropriation of behaviors and modes of thinking and acting that make each child governable.
As an example of bio-power, we can mention all the recent emphasis on measuring and evidence based research that reduce full human beings to numbers representing mathematical performances. The mass scale comparative studies as the Trends in International Mathematics and Science Study (TIMSS) and the OECD’s Program for International Student Assessment (PISA) represent the most prominent manifestation of this phenomenon. These international, comparative, measurement studies are to an increasing extent brought into the political sphere placing pressure on national governments to regulate their educational systems according to the standards stipulated by those tests (Biesta, 2009; Wilson, 2007). This is what has been happening in the last eight years in very many developed countries where education tends to be transformed, by the pressure of politicians’ demands for accountability, into an evidence-based profession. Consequently, political measures contribute to formatting teaching and learning of mathematics in a clear and crude way. Teachers tend to tailor their instructional practices to the format of the test out of concern that if they design their teaching differently, their students will fail. Although they might know all the didactical novelties and methods to promote learning in a way meaningful to the students, if what counts is to pass the test, that is how they will ‘educate’ their students (Wilson, 2007; Lerman, 1998).
The interplay between these two mechanisms of subjectification —techniques of subjective individualization and procedures of objective totalization— creates a twofold political strategy which Foucault (1978) calls bio-politics: the growing inclusion of man’s natural life (as opposed to his political life) in the mechanisms and calculations of power. Politics is made operational. Its purpose is no longer to be a place where alternative emancipatory ways of living together can be thinkable, but to engage in the global regulation for the sake of the specie(s). For Agamben (1998), who amplified the work of Foucault, the only real question to be decided is which form of organization would be best suited to the task of assuring the care, control and use of what he calls bare life: life stripped from its entire political dimension, and reduced to a biological entity likely to be measured, calculable, predicted – the object of technical expertise. It is in this sense that Žižek (2006) affirms that today we live in a post-political society: politics give place to specialized social administration, targeting the bare life of the individual by controlling its fluctuations according to global standards of normality.
Just as politics is being replaced by administration, education is giving place to specialized pedagogy and didactics. Valero’s (2004) description of the “cognitive subject” is a good example of the way mathematics education research reduces a full human being to a bare student, whose cognition can be scrutinized for the aim of learning mathematics. All the complexity of the social and political life of the student is wiped out. The student is reduced to a biological entity, likely to be investigated in a clinical way.2
RESEARCH ON EQUITY We argue that education has increasingly been thought of as an operational framework for the individual’s subjectification. In the next pages we want to explore how research on equity can also have a propensity to engage on research that keeps unaddressed problems that by its very nature requires for theories that are far from being recognize as theories of mathematics education.3
Although the understanding about what it means to achieve equity diverge, and some authors prefer to use other terms as social justice (e. g. Gutstein, 2003), democratic access (e. g. Skovsmose & Valero, 2008), inclusion/exclusion (e. g. Knijnik, 1993), it is common to acknowledge that research on equity requires social and political approaches that situate the problem in a broader context than the classroom or schools (Anderson & Tate, 2008; Gates & Zevengergen, 2009; Valero, 2007; Gutiérrez, 2007; Nasir & Cobb, 2007b). For instance, Nasir and Cobb (2007a) state that all the contributors of the book Improving access to mathematics: diversity and equity in the classroom “view equity as situated and relational and as being informed both by local schooling practices and by practices and ideologies that transcend school” (p.5). However, by reading the different contributions of the book we realize how all the research done is centered on improving the process of teaching and learning mathematics. Although politics is acknowledged as determinant in equity, and some authors explore this connections between mathematics education and politics (e.g. Gutiérrez), it lacks a theoretical analysis on how these “ideologies than transcend school” influences what is happening in schools, and how it contributes or not to equity. As mentioned by Gutiérrez (2007) in the same book “little has been written in mathematics education that addresses how mathematics might play a role in broader politics” (p. 38).
One of the most extensive reviews on the issue of equity in mathematics education is the article by Bishop and Forgasz (2007) published in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007). The authors try to give us an overview of the different research approaches on the issues of access and equity in mathematics education. Right from the beginning they call our attention to the artificiality present in the construction of groups of people as being in disadvantage (girls, ethnic minorities, indigenous minorities, western “ex-colonial” groups, non-Judeo- Christian religious groups, rural learners, learners with physical and mental impairments, and children from lower class) and how such constructions can in themselves convey discriminatory actions. This
2 An alluring analogy made by Silver and Herbst (2007) between mathematics education and medicine makes evident how this trend is full alive in mathematics education research. The authors place mathematics education as a science of treatment, and by understanding the symptoms that characterizes the difficulties of students’ learning of mathematics we can propose the proper treatment: “The evolving understanding of the logic of errors has helped support the design of better instructional treatments, in much the same way that the evolving understanding of the logic of diseases has helped the design of better medical treatments” (Silver & Herbst, 2007, p. 63). In this perspective, students are seen as patients in need of treatment, and the role of mathematics education is to understand students’ problems and elaborate designs that threat those learning diseases. 3 For an account on the different theories being used in mathematics education research see Cobb(2007), Silver and Herbst (2007), or the publications resulting from the Survey Team of ICME11 on The notions and roles of theory in mathematics education research, coordinated by Teresa Assude, Paolo Boero, Patricio Herbst, Stephen Lerman and Luis Radford. problem has been recently labelled by Gutiérrez (2008) as the “gap-gazing fetish in mathematics education”, which provided a interesting discussion between Rochelle Gutiérrez and Sarah Lubienski, published in the Journal for Research in Mathematics Education, where the two authors confronted their ideas and different strategies of approaching the issue of equity. Roughly speaking, the dilemma is how to know if a research based on an achievement-gap focus can benefit or not the purpose of equity. The position of Gutiérrez (2008) is that there are dangerous in conceiving and performing research focused on an “achievement gap”. These dangerous include
[O]ffering little more than a static picture of inequities, supporting deficit thinking and negative narratives about students of color and working-class students, perpetuating the myth that the problem (and therefore solution) is a technical one, and promoting a narrow definition of learning and society. (p. 358)
The author argues that such research, which usually leans on quantitative methods of data collection, does no more than providing a description of the problem without presenting understandings that allow us to change it. She argues that less research should be made focusing in the “gap”, and more research should be focused on the qualitative analyses of successful experiences among groups of people considered to be in disadvantage.
On the other hand, Lubienski (2008) assumes the position that research in gap analyses is necessary. She is against the suggestion of Gutiérrez of lowering the intensity of gap analyses, but argues to move towards a more skilled and nuanced analysis: “analyses of gaps also inform mathematics education research and practice, illuminating which groups and curricular areas are most in need of intervention and additional study” (Lubienski, 2008, p.351).
Lubienski is concerned with the question “Is there a gap?”, to what follow all the studies that analyses when those gaps begin, under what conditions they grow or shrink, and what consequences underserved students ultimately suffer because of the gap. Whereas Gutiérrez is concerned with the question “How to diminish the gap?”, to what follow studies orientated towards effective teaching and learning, making research more accessible to practitioners and more intervention by the researcher.
Although we can discuss the better ways to do research in equity, there is a fundamental question that cannot be left unaddressed: Why is there a gap at all? That is, why do school (mathematics) systematically excludes and includes people in the network of social positioning? Why do schools perform this selective role that inevitably creates inequity? As Bishop and Forgasz (2007) put it, “in every country in the world mathematics now holds a special position, and those who excel at it or its applications also hold a significant positions in their societies” (p. 1149). Why our society needs to have such an institution that guarantees from very early ages an accumulation of credit? 4 This question is rarely posed by the community of research in mathematics education when addressing equity. By posing it we dangerously open the field of education to politics.
Although the issue of equity is usually conceived as having to do with specific groups of people (women, indigenous, poor, etc), other issues are at stake. Valero (2007) analysed a paradigmatic episode of discrimination in a regular Danish mathematics classroom. The case of the “lonely girl” (p. 227) is about Gitte, a Danish teenager which was posit by the school administration and by her teacher
4 For what we know, it was Shlomo Vinner (1997) who introduced the idea of school as a credit system. For a deeper analysis on how schools are permeated by the capitalist way of living in the field of mathematics education research see Baldino and Cabral (1999). as a student with learning difficulties in mathematics. The girl was isolated in the classroom, performing banal tasks like sharpener the rulers for her colleagues or pick up dropped pencils. She was allowed to be in school, but everybody unassumingly knew she was not learning any mathematics. The exploration of these cases led Valero to assert that “disadvantage is being built even at the heart of an educational system that has inclusion and democracy as an organizational principle” (pp. 228, 229). The problem of equity is not exclusive of people who are positioned as being in disadvantage due to their association to some category (ethnicity, gender, linguistic, socio-economical, etc.). Indeed, we wish to argue for a displacement of the problem of equity that conceptualizes inequity not so much as a problem affecting particular groups of people, but a generalized problem in the school system, who affects everyone by the way schooling is involved in the social stratification. The antagonism is that such systematic “social selection” is happening at the core of a school organized around democratic and inclusionary principles.
Some authors have been trying to list which practices can be carried out in order to achieve equity. For Schoenfeld (2002, quoted in Langrall, Mooney, Nisbet, & Jones, 2008, p. 127), achieving equity requires four systematic conditions to be met, namely, 1) high quality curriculum; 2) a stable, knowledgeable, and professional teaching community; 3) high quality assessment that is aligned with curricular goals; and 4) stability and mechanisms for the evolution of curricula, assessment and professional development. Alternatively, Lubienski (2002) claim that, concerning the issue of equity, the goal is to learn more about the complexities of successful implementing meaningful instructional methods equitably with students who differ in terms of social class, ethnicity and gender. Or, according to Goldin (2008), “to create teaching methods capable of developing mathematical power in the majority of students” (p. 178). Finally, Gates and Zevenbergen (2009) identify a common basis for how to deal with equity that in some way resume the research made in mathematics education
What might we all agree on then as fundamentals of a socially just mathematics education? Perhaps we can list: access to the curriculum; access to resources and good teachers; conditions to learn; and feeling valued. (p. 165).
The first thing that pups our eyes is the complete absence of a political conceptualization of the problem of equity. What is recognized as an economical and political problem, end up being researched as a problem entirely entangled by mathematics education. The problem of equity is reduced to a problem of developing the best “instructional methods” to allow mathematical success to all students.
WHAT DOES QUALITY MEANS? There are at least two dimensions in which we can address the issue of quality in mathematics education. On the one hand, we have the quality inherent to the mathematics education of people, which has school mathematics as the primordial referential. On the other hand, we can also refer to the quality of mathematics education research itself. Although is out of the range of this paper to analyse in dept the different understandings that different groups of people attribute to quality in these two different contexts, we can identify common shared assumptions concerning what it means quality both in terms of school mathematics and research.
Concerning the latter, there has been a long discussion in the mathematics education research community on how to develop research that could be considered of quality (Sierpinska & Kilpatrick, 1998, Menghini, Furinghetti, Giacardi, & Arzalello (2008)). Although research approaches may vary, both theoretically and methodologically speaking, there seems to be a consensus that the main concern of mathematics education research is to improve students’ performance in mathematics. Niss (2007) is very clear when answering the question of why do we do research in mathematics education: “We do research on the teaching and learning of mathematics because there far are too many students of mathematics, from kindergarten to university, who gets much less out of their mathematical education than would be desirable for them and for society” (Niss, 2007, p. 1293). If this is the main concern of mathematics education research, it is not surprising that the field has been designed as a space for researching “the problems of practice” (Silver & Herbst, p. 45), defined as problems relating to teaching and learning, in a systematic, scientific way. According to Boero (in press) “this is a rather obvious widely shared position” (p. 1). In this framework, the work of mathematics educators is “to identify important teaching and learning problems, considerer different existing theories and try to understand the potential and limitations of the tools provided by these theories” (Boero, 2010, p. 1). Following this line of thought, Cobb (2007) suggests that mathematics education should be understood as a “design science” (p. 7), and provides as an example the NCTM standards. By design science Cobb understands “the collective mission which involves developing, testing, and revising conjectured designs for supporting envisioned learning process” (p. 7). The ultimate goal of a science designed this way will be to “support the improvement of students’ mathematical learning” (p. 8).
A quality mathematics education research seems to be the one that allows students to improve their mathematical performance. This leads us to the second way in which we can talk about quality: what does it means for students to achieve a quality mathematical learning? The literature on mathematics education research is full of statements that posit mathematics and its education as powerful knowledge and competence to become a full citizen and worker. These two educational functions, that Biesta (2009) calls qualification - having to do with the need for having people with the knowledge, skills and understanding that allow them to ‘do something’ in a professional basis; and socialization - having to do with the role of education in allowing people to become members of a particular society, by the insertion of the ‘newcomers’ into existing social and cultural orders; compound the two main goals of mathematics education:
Mathematics education in schools is thus seen to have a dual function: to prepare students to be mathematically functional as citizens of their society [the socialization function] – arguably provided equitably for all – and to prepare some students to be the future professionals in careers [the qualification function] in which mathematics is fundamental, with no one precluded dorm or denied access to participation along this path. (Bishop & Forgasz, 2007, p. 1152)
On the one hand, mathematics education is important because allows the nurturing of the next generation of mathematicians and those who will use mathematics in their work, therefore assuring the development of a working force equipped to compete successfully in the global economy of our high-tech society. On the other hand, mathematics educations assure the insertion of people into a society where mathematics is seen as an indispensable tool to become a citizen. The goal of citizenship concerns a wide range of competences: providing mathematical skills for dealing with situations of everyday life, intellectual enrichment, acknowledging mathematics as equally a part os humankind’s cultural and aesthetic heritage, or making accessible powerful tools to analyze, critique and act upon the way mathematics is used in society as “mathematics in action”.
The way quality is understood both in mathematics education research and in school mathematics seems to be in consonance. Since school mathematics is posited as indispensable to become both a productive and competent worker and an active and participative citizen, the purpose of mathematics education research should be to improve students’ mathematical learning. What this way of conceiving quality conceals is the ideology informing what it means to be a worker and a citizen in a capitalist society.
THE IDEOLOGY BEHIND THE DISCOURSES ON QUALITY At first glance, the aims for school mathematics mentioned above are worthy aims for any compulsory schooling system. Becoming a well succeeded worker and, moreover, an informed and participative citizen seems to fulfil the desire of students, parents, politicians, teachers and others participants in the educational process. So why do we feel uneasy about these aims? Partly because the listed aims for school mathematics seem to be thought having in mind the idea of a subject conscious of himself (Althusser, 2000), therefore, disavowing all the political substrate that inform what it means to be a worker and a citizen in current societies. On the other hand, because these aims conflict with the politics of accountability where quality is often defined as having the best ranking positions both in national and international examinations. Allow us to explore these two aspects in more detail, by relating them with the ideology behind capitalism.
In his essay about the relation between the works of Karl Marx and Sigmund Freud, Althusser (2000) identifies the ideology of capitalism as the one that conceives the individual as a subject conscious of himself. According to this ideology, man is defined as the self-conscious subject of his own necessities: nothing escapes from man’s consciousness that cannot be accomplished by the deployment of his own consciousness. The reason why this is the ideology of capitalism is because capitalism requires a subject who sees himself as conscious and responsible for their own acts, so that it can be persuaded, in conscience, to obey the rules that other way should be imposed by force, therefore less economical. The decisive importance of Karl Marx’s5 work was having shown us that, contrary to the assumption that the subject is the master of his actions, the subject is not conscious about the ‘nature’ of the place he occupies in the structure characterized by the laws of capitalist society. With Marx we understand how behind the ideology that asserts the equality of individuals in the free market lies a profound inequality. This inequality is generated by the appropriation by the capitalist of the work of others, therefore generating capital.
In the case of the aims for school mathematics, the question to be made is what it means to be a worker and a citizen in our current capitalist society? One of the ideological modes dissected by Žižek (1994) conceives ideology as “a doctrine, a composite of ideas, beliefs, concepts, and so on, destined to
5 Together with the work of Freud, which forever dispossesses the subject from the safe place of a self-conscious subject. Freud showed us that there is a discrepancy which is repeated between what the individual wants to say and what he actually says. According to Miller (1999) it is in this discrepancy that Freud situated what he called the “unconscious” – as if for this wanting-to-say of mine, which is my “intention of signification”, another wanting-to-say was substituted, which would be that of the signifier itself and which Lacan designated as “the desire of the other”. Both Marx and Freud displace the human being from the position of the subject conscious of himself, therefore, striking the strongest criticism on the foundations of capitalist ideology. convince us of its ‘truth’, yet actually serving some unavowed particular power interests” (p. 10). The strategy to criticize this mode of ideology is to carry a symptomal reading (Althusser, 1994) that exhibits the discrepancies between the public discourse and the actual intention of it. The NCTM (2000) standards are a prolific document to engage in such a reading. Some authors already did that (e. g. Skovsmose & Valero, 2008) and it basically consists in showing how behind the public discourse of forming students to become active and participative citizens in societies, there is a concern in maintaining United States’ level of economical and scientific dominance. NCTM standards are also a case of what Žižek (2005) called staged democracy. We can find in the official discourse all the virtues and democratic goals that we stand for, but, in practice, these aims continue to fail. In this case, the ideological critique will be concerned not in understanding how in practice those desirable aims continue to fail (equality among people, dignity, etc.) – as if it were a problem of “applicability” – but to understand how the discrepancy is already being created at the level of the official discourse by completely obliterating the real reasons why it continues to exist inequality and lacks of democracy.
However, in order to become efficient, ideology must go under a process of ‘self-disguising’, so that we can be able to act as if our actions were deprived of all ideological content: “the very logic of legitimizing the relation of domination must remain concealed if it is to be effective.” (Žižek, 1994, p. 8). We must not perceive ourselves as being interpelated by some big Other 6 but as individual subjects who freely choose to belief and act according to utilitarian and/or hedonistic motivations. When NCTM argues for the importance to educating students to become active participants in society, they disregard any pathetic ideological phrases in sustaining their argument. The argument is or a pragmatic one – we need competent people in mathematics to become the future workers of our high- tech society – or a hedonistic one – people get empowered through mathematics. What we cannot miss here is that this attitude remains an ideological one: it involves a series of ideological presuppositions (e. g. about what it means to be an active citizen in a more and more commoditized society) that are necessary for the reproduction of existing social relations. A staged discourse is needed so that school mathematics continues to perform others roles than those present in the official discourse.
On the other hand, how does one can assess the quality of students’ mathematical learning? It seems to be an unachievable task to assess if students become or not the desirable workers and citizens. Apparently there is no possible way of assessing the quality of the mathematical education of students. However, society cannot live in this state of uncertainty regarding the mathematical performance of students. Society craves for results, for evidence that shows if people are or are not becoming the desirable subjects. Therefore, a rigorous instrument should be created so that we can objectively know if students are performing well in school mathematics. Indeed, such instruments exist under the form of well known global examinations. We risk saying that in our days where accountability reigns, what counts as quality is the performance of students in global examinations. Ultimately, are not the results from these examinations what defines if a mathematics education is or is not of quality?7 So we are confronted with the inconsistency of a system that, on the one hand, defines quality as a matter of achieving the desirable “mathematical subject” – informed worker, critical citizen– on the other hand,
6 In this context, the Lacanian notion of big Other stands for all the State, Justice and Law that give symbolic meaning to our social life. 7 And, by extension, the national examination and the classroom testing as the forever lasting method for evaluate students’ mathematical learning. what ultimately decides the quality of mathematics education is the results of the exam. Again, the question to be posed is why do we need such a staged discourse concealing what everybody knows8?
MATHEMATICS EDUCATION AND ITS SPECIFICITY Although studies dealing with equity in mathematics education acknowledge the social and political dimension of the problem (especially in the beginning and the end of the texts), we argued that they manifest signs of persistence as if the problem of inequity could be understood and solved within mathematics education. It is as if we admit that the problem as a social and political nature, residing way beyond the classroom, but, since we are mathematics educators, we must investigate it in the classroom. As stated by Gates and Zevenbergen (2009) “mathematics and social justice has been the focus of much research – however this has largely focussed on such issues as the process of learning, the content of the curriculum and its assessment.” (p. 162). They also make a very suggesting point. They argue that it is common in mathematics education research to discard such “political” questions since it is not the responsibility of mathematics education to address them (p. 165). This position is related with the way researchers conceive the field of mathematics education research.
As we saw, the mathematics education community broadly acknowledges that the purpose par excellence of mathematics education research entails the process of teaching and learning mathematics (Cobb, 2007; Silver & Herbst, 2007; Boero, 2010; Sfard, 1998; Sierpinska & Kilpatrick, 1998). One of the specificities of the field is the fact that it is mathematics education, and not other education. In this way, mathematics is posited as the “thing” that differentiates mathematics education research from science education, for instance: “[a]ny discussion of research in mathematics education must occur in a context involving mathematics (…) One is looking at mathematics learning, and one cannot ask these questions outside mathematics” (Sierpinska & Kilpatrich, 1998, p. 25). Although it seems clear that learning mathematics is different from, for instance, learning music, we think that there are important common educational problems that outweigh the specific problems of some school subject. Indeed, we argue that if mathematics education research remains attached to the specificity of mathematics important educational problems will continue to be unaddressed. One of these problems is related with achieving equity, which is recognized by the community to be a problem that transcends mathematics education. The question to be posed is: if we admit equity to be a problem that surpasses the field, how does mathematics education research address this “extra” dimension of the problem if it remains attached to the specificity of mathematics? What is at stake here is recovering the educational dimension of mathematics education. That is, recognize and engage in mathematics education as a political task, where the problem of equity can only be fully addressed if we open our research to more than developing instructional design and teaching.
This interplay between the specificity of mathematics and the generality of education is not new. Already Freudenthal (1981) in his listing of the mathematics education problems, states that “[i]n a
8 Especially teachers in schools. They know that apart from all the efforts to allow students with a mean full mathematics education experience, ultimately what counts and on which their evaluation will depend of is the national result of students’ exams. How many times a teacher who wants to flower some explanation (a little bit of history, an application, a connection with other themes, a more insightful explanation) heard the students promptly ask “will that show in the test, teacher?” And the teacher is forced to say “well, yes” if maintaining students’ attention is in the agenda. sense the title of my address [Major problems of mathematics education] is wrong: all major problems of mathematics education are problems of education as such. In another sense” he continues “it is exactly right: if you look for major problems the best paradigms of cognitive education is mathematics” (p. 134). Freudenthal acknowledges that all major problems of mathematics education are educational problems, therefore, not specific of mathematics education. On the other hand, he also acknowledges that there are educational problems where mathematics has been a fruitful case study. 9 We read in this sentence a willing to keep the field of mathematics education research open to a conceptualization of its problems not just as “learning” problems but as educational ones. Indeed, this appeal was made by Freudenthal himself in his well known refusal to talk in terms of “curricular development”. For him the purpose of research is “educational development” (p. 135).
THE DISAVOWING OF POLITICS IN MATHEMATICS EDUCATION
While for a teacher in the old school it was clear that school success was not available to all pupils, the new teacher, believing in the egalitarian omnipotence of the school as an institution and in the science-legitimated humanism of academy pedagogy, promises salvation for every child. (Simola, Heikkinen & Silvonen, 1998, p. 81)
In contrast to the old elitist view of teaching, where it was assumed that school success was just for some privileged pupils, in our days the ideological discourse assumes the premise that mathematics is for all and that no child should be left behind. In order to satisfy this societal demand, fields of expertise like mathematics education are called to investigate new ways of assuring mathematical success to all students. As we know, in the last two decades there has been a huge increasing amount of research on equity. As Baldino and Cabral (2006) mentioned, we have today a considerable array of research covering the mechanisms of social exclusion, initiatives for change, detailed and in depth studies, comprehensive and interactive studies and data, new teaching strategies, and, recently, growing numbers of studies addressing the social and cultural aspects of school mathematics. However, in spite of all these research efforts the social gap continues to increase. Baldino and Cabral (2006) raise the question: “why do so many people insist in asking for more that which cannot be said to have produced results for change so far?” (p. 21). This is, we think, a major topic for reflection in mathematics education community. 10
In the remaining pages we will explore some theoretical considerations regarding the disavowing of politics involved when addressing the issue of equity from a restricted perspective in mathematics education. We argue that this attitude of political disavowal keeps research at a “technical” level, hence running the risk of ending up having different results from the ones it aims for. Furthermore, we argue that this is one of the strongest limitations for bringing equity and quality together. A quality
9 Piaget is the most known example in cognitive psychology. However we can also mention Jean Lave in situated learning, Valerie Walkerdine in discourse studies, Thomas Popkewitz in political sciences, or Leslie White in anthropology. 10 In last ICME11, in México, during a plenary debate session with Paul Cobb, Mariolina Bussi, Teresa Rojano and Shiqi Li, entitled What do we need to know? Does research in mathematics education address the concerns of practitioners and policy makers?, Shiqi Li asked a very insightful (and provocative) question: Why does the students of the research always increase their capabilities (to solve problems, to learn with meaning, of communication, to use technology, etc.) but in reality, in the daily routine of worldwide classrooms, failure in mathematics persist, and students are far from reaching those desirable capabilities achieved in research settings? 11 mathematics education is not one that attends mainly to the intrinsic characteristics of mathematics as the foundations for educational practices, but rather one type of education that recognizes the possibilities of the school subject within the social, political and historical frame in which it is being constituted. This means that a definition of quality in mathematics education that does not attend to how it is shaped in power relationships is a partial definition that can only place hysterical demands to teachers. We will lean heavily on the philosophy of Slavoj Žižek, especially the analysis he makes on how ideology works today.
We saw how researchers comply with the societal demand of mathematics for all. They engage on this demand by assuming that through their studies on teaching and learning, on better curricular and instructional design, on better connections between researchers and practitioners, they are contributing to achieve equity in school mathematics. However, if equity is an economical and political problem that escapes school, then the society´s demand is a hysterical one, that is, impossible to satisfy (cf. Žižek, 1991). Why then do we keep doing research as if the problem could be solved within mathematics education? Could it be that by keeping us occupied doing innocuous research inhibits us from looking at other issues?
How to read the recent governmental pressure to develop “pragmatic” educational research, evidence- based, ready to apply? As we are living in an époque where time is money, why lose money with all this philosophical waste of time? What we need, they say, is engagement into action, quick solutions ready to be implemented, evaluated and, eventually, discarded, so that the all process can start again. We argue that this pressure to produce “evidenced-based research” is part of an ideological injunction to keep us occupied with specific research, while neglecting research that is not immediately concerned with providing solutions but to complicate the usual ways we approach the problem. Žižek (1992) states the same apropos the way social, cultural and political studies engage on research:
When, in a critical analysis of the present global constellation, one offers no clear solution, no ‘practical’ advice on what to do, when one paints no light at the end of the tunnel (well aware that this light might belong to a train crashing towards us), one is usually reproached: “So what should we do, nothing? Just sit and wait?” One should gather the courage to answer: YES, precisely that! There are solutions where the only truly ‘practical’ thing to do is to resist the temptation to engage immediately, and to “wait and see” by means of a patient critical analysis. (p. xv)
As we know, dominant social systems demand for perpetual reforms by means of integrating what could be new and potential emancipatory acts into well establish social structures. In other words, dominant systems, as today’s capitalism, need to constantly change something so that nothing really changes (Žižek, 1991). In the set of these superficial transformations, as Paulo Freire called them, are part of the novelties research produces on how to promote equity by improving the teaching and learning of mathematics.
According to Gutiérrez (2007), “[e]quity is threatened by the underlying belief that not all students can learn” (p. 3). Although in a first reading we agree with Gutiérrez, we think other believes are at stake, namely the not underlined but publicly assumed belief that all students can learn. The interplay between these two discourses - the official one, present in curriculums, political documents and research, attesting that mathematics is for all, and the commonly shared but not assumed belief that there will always be some who will fail – makes visible how ideology works today. Following Žižek’s (2010) thought, when we read an abstract ‘ideological’ proclamation such as “mathematics for all”, we are well aware that this is not how teachers and students in schools experience it: in a class of thirty students there will always be those who fail in mathematics. The official discourse functions not as some kind of utopian state to be achieved, but purely to conceal the fact that mathematics is not for all. Such an erasure of the “background noise” – the voices of those who will always fail – is the very core of utopia. What this “background noise” conveys is “the obscenity of barbarian violence which sustains the public law and order” (Žižek, 2010, p. 10). In the case of education, the obscenity of a school that year after year throws to the garbage bin of society thousands of people, under the official discourse of an inclusionary and democratic school.
If we know that while society remains organized around capitalist tenets11 there will always be exclusion and, particularly, students failing in mathematics, why do we need an official version assuring us that mathematics is for all, that is, covering up what everybody knows? Because it covers a bigger lie. The capitalist lie that presupposes equity in schools (as an extension of the equality in the market). In other words, the official discourse conceals the inconsistency of a system that, on the one hand, demands mathematics for all and, on the other hand, uses school mathematics as a privileged mechanism of selection and credit.
This denial in confronting the real core of the problem of equity is the result of an ideological injunction that systematically lead us to repeat the same “abstract” discourses – school as an place for emancipation; mathematics as a powerful knowledge and competence; mathematics for all, etc. In order to critically analyze such discourses we should replace the abstract form of the problem with the concrete scenes of its actualization within a life-form:
In order to pass from abstract propositions to people’s ‘real lives’, one has to add to the abstract propositions the unfathomable density of a life world context – and ideology are not the abstract propositions in themselves, ideology is this very world density which ‘schematizes’ them, renders them ‘livable’.” (Žižek, 2010, p. 6)
That is to say, in order to understand which are the real aims for school mathematics, or the real motives that students have to be in school, we must not repeat ideologically loaded discourses conveyed by the curriculum, by political statements, and even by the research, but to look the “negative” - schools sorting the future people for the labor market by means of credit accumulation - in the face and convert it into being. That is, what Gutiérrez calls the “underlying believe that not all students can learn” must be posited not as a threat to equity, but as the truth of a system in which equity is forever postponed. Following Žižek’s (1988) thought, this implies research to pass from the notion of crisis (in this case, the fact that people fail is school mathematics therefore creating exclusion) as an occasional contingent malfunctioning of the system, to the notion of crisis as the symptomatic point at which the truth of the system becomes visible.
Some will say that such an awareness of the problem of equity takes us to a deadlock. Indeed, by realising that exclusion is something inherent to the school system we realise that to end exclusion means to end schooling as we know it. In the current myriad of world social structure this does not seems possible. However, what dooms us to repeated failure is precisely experiencing the change as impossible - we acknowledge that the problem of equity requires a fundamental societal change which
11 We know since Marx that sub development and exclusion are not malfunctions of capitalism, but the proper conditions that keep it alive. For a recent discussion on this issue see Žižek (1988). we experience as impossible. The question is: is it impossible or it is ideologically posited as impossible?
THRESHOLD The key feature here is that to see the true nature of things, we need the glasses [glasses as a metaphor for critical ideological analysis]: it is not that we should put ideological glasses off to see directly reality as it is: we are ‘naturally’ in ideology, our natural, immediate, sight is ideological. (Žižek, 2010, p. 6)
We argue that mathematics education research needs such glasses. The ‘natural’ way in which we relate with reality is ideological - in our practice we convey discourses that conceal more than what we know. Ultimately, the purpose of this article was to essay what could be such ideological critique in the way we address issues of equity and quality in mathematics education research. Apparently, there is no doubt that definitions of quality and the discourses for equity live side by side and are equally political. However, it is almost inexistent in mathematics education research studies that aim to understand in dept such problems that are identified as political in their nature. If mathematics education research desires to address them, it must open its gates to research that locates the complexity of mathematics education within the network of social and political practices that permeate all educational act. Without that we run the risk of falling in the trap of what we criticize. On the issue of equity, our premise is that exclusion and inequity within mathematics education and education in general is an integrative part of current school education, and cannot be conceptualized without understanding the relation between school education and the social mode of living that characterizes actuality: capitalism. On the issue of quality, a serious challenge is also to politicize our understanding of what is taken to be the significance of valued forms mathematical thinking within capitalism.
Therefore, our intention with this text is not to give a solution for the problem of equity and quality, neither it is to open an alternative way of doing research on these topics. Our purpose is much more modest. We wanted to raise an awareness that there is broader issues involved when discussing equity and quality in mathematics education than doing research on better ways to teach and learn mathematics, where the main focus is to improve students’ mathematical performance so that they could, through mathematics, become better workers and citizens. As mathematics education researchers actively engaged in the field, we find the need for developing a deeper understanding of our practices and the discourses we convey. The way we found to do this was to explicitly look at the inconsistency of discourses that make the apologia of equity and quality without having in consideration a deeper analysis of the meaning this terms have in a society where capitalism has become the ontologized substrate for all social relations.
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